The selection of charged tracks, photons, and \(K_S^0\rightarrow \pi ^+\pi ^-\) 
candidates are described in Refs. [1]}, [2]}. A candidate
\(\pi ^0~(\eta )\)  is reconstructed from a pair of photons with an
invariant mass in the range \(|M_{\gamma \gamma }-m_{\pi ^0}|<\) 15 MeV/\(c^2\) 
(\(|M_{\gamma \gamma }-m_{\eta }|<\) 15 MeV/\(c^2\) ), where \(m_{\pi ^0}~(m_{\eta })\)  is
the nominal \(\pi ^0~(\eta )\)  mass [3]}.
The event candidates of \(e^+e^-\rightarrow \pi ^{0}\pi ^{0}h_{c}\) , \(h_c\rightarrow \gamma \eta _c\)  are required to have at least one
\(\gamma \pi ^0\pi ^0\)  combination with the mass recoiling against
\(\pi ^0\pi ^0\) , \(M_{\pi ^0\pi ^0}^{\rm recoil}\) , in the \(h_c\)  mass region
(\(M_{\pi ^0\pi ^0}^{\rm recoil}\in [3.3,3.7]\)  GeV/\(c^2\) ) and with the mass
recoiling against \(\gamma \pi ^0\pi ^0\) , \(M_{\gamma \pi ^0\pi ^0}^{\rm recoil}\) , in the \(\eta _c\)  mass region ( \(M_{\gamma \pi ^0\pi ^0}^{\rm recoil}\in [2.8,3.2]\)  GeV/\(c^2\) ).
